Geometric fundamental reactor types

In Chapter 4, we shall expand our knowledge of the geometric viewpoint to include reaction, and describe the function of three fundamental reactor types that are used in AR theory. With this knowledge, we will be in a position to generate candidate ARs efficiently, and use this information to form optimal reactor networks, which may be applied to optimize complex reactive systems. 

In much the same way that concentration can be viewed as a vector, it is possible to view a system of reactions as a vector as well. We now wish to explain how well-known reactor models, often studied in undergraduate chemical reaction engineering courses, can also be interpreted geometrically. In this section, we would like to describe the behavior of three fundamental reactor types PER, CSTR, and DSR. 

Now that the physical, mathematical, and geometric nature of all three fundamental reactor types used in AR theory has been detailed, it is usehil to provide a summary of the results. Table 4.5 may be used as a point of reference for the problems that are described in later chapters. The ideas described in previous sections form the foundations of AR theory, and hence it is important that these concepts are understood well. 

The three-dimensional Van de Vusse system is considered a complete system in AR theory. The AR for the system is well understood and can be generated with confidence. This construction allows us to demonstrate (geometrically) the role that all three fundamental reactor types play in the formation of the AR boundary. It is not always easy to identify, beforehand, whether the true AR has been found or not, and thus this example is convenient because the true AR is guaranteed by theory. 

Chapter 4 extended our understanding of the geometric viewpoint to include reaction. Systems of reactions, together with reaction stoichiometry, may be interpreted geometrically in the form of rate vectors, which allows us to view fundamental reactor types as geometric processes. 

Reaction may also be interpreted geometrically. Rate vectors are nsed to describe how reactions can be used to move through concentration space. Three fundamental reactor types are employed in AR theory the PFR, the CSTR, and the DSR. No other reactor type is required to generate the AR. Each reactor type exhibits its own characteristic geometric interpretation and each performs a crucial function in bnilding different parts of the AR bonndary. 

Chapter 4 In this chapter, we discuss how reaction may also be viewed from a geometric perspective. We introduce the three fundamental reactor types used in AR theory, and we also discuss additional properties of the AR related to reaction. 

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